「純正律」の版間の差分

この単純な関係は、初めて聞く人にとってはなかなか信じがたいかもしれません。それがほかの思い付きと一緒くたになれば混乱もするでしょう。はい、これは驚異的なことです。でもすべての音がこういうスペクトルを持つわけではありません。<ref>鐘やゴングなどの打楽器、それにシンセサイザーの音は、独自の複雑なスペクトルを有します。インハーモニックな音はまた楽音なスペクトルの中から見つかる場合もありますし、楽音を出す楽器でもアタックの部分ではインハーモニックなスペクトルを示す場合があります。金管楽器を強く演奏すると、アタック部分では倍音がより高い周波数で鳴り、その後ノイズ(噪音)を伴いながら周波数が低下して定常状態の楽音になります。 A breathily played flute has a large addition of inharmonic material, a "jinashi" shakuhachi flute is an excellent example of an instrument of varying harmonicity and inharmonicity.</ref>

In a tuning "according to the natural scale", we have for example a "perfect fifth" as simply the ratio between the third partial and the second partial: "3:2". In our example tone, that would be the ratio of 300 Hz to 200 Hz. Were we to want a just intonation perfect fifth above our original tone, its fundamental frequency would be found at 3/2 times the fundamental frequency of our original tone. So, 3/2 times 100 gives us 150. Our example perfect fifth has a fundamental frequency at 150 Hz.

<pre>Tone   Frequencies of partials (Hz)

Do     100  200  300  400  500  600  700  800  900  ...

So     150  300  450  600  750  900  1050  1200  1350  ...</pre>

You see that the tones share the frequencies of some of the partials. These partials will "meld" when our Do and Sol are played together. This goes by the wonderful name of ''Tonverschmelzung'' in German. It is a very distinctive "blending" sound. If our Sol was tuned to, for example, 148 Hz, its second harmonic component would be at 296 Hz, and the two tones played together would not "meld together" at 300 Hz, but would "beat". That is, we would hear a throbbing sound, the "beat rate" of which is found by reckoning the distance in Hertz between the two near-coincident partials. In this case, 300 - 296 = 4 Hz, so we'd hear a beating of four times a second (this is like a rhythm of eighth notes at a metronome marking of 120 beats per minute).